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April, 1995 Stochastic Integration of Processes with Finite Generalized Variations. I
Nasser Towghi
Ann. Probab. 23(2): 629-667 (April, 1995). DOI: 10.1214/aop/1176988282

Abstract

In this paper the $L^1$-stochastic integral and the mixed stochastic integral of a process $Y$ with respect to a process $X$ is defined in a way that extends Riemann-Stieltjes integration of deterministic functions with respect to $X$. The $L^1$-integral will include the classical Ito integral. However, the concepts of "filtration" and adaptability do not play any role; instead, the $p$-variation of Dolean functions of the processes $X$ and $Y$ is the determining factor.

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Nasser Towghi. "Stochastic Integration of Processes with Finite Generalized Variations. I." Ann. Probab. 23 (2) 629 - 667, April, 1995. https://doi.org/10.1214/aop/1176988282

Information

Published: April, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0830.60047
MathSciNet: MR1334164
Digital Object Identifier: 10.1214/aop/1176988282

Subjects:
Primary: 60H05

Keywords: bimeasures , Frechet variation , generalized variations , Riemann-Stieltjes sums , stochastic integration

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 2 • April, 1995
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